# What is the Cartesian form of ( -2 , ( 7pi)/3 ) ?

Apr 20, 2018

The Cartesian form is $\left(- 1 , - \sqrt{3}\right)$

#### Explanation:

$x = r \cos \theta$

$= - 2 \cos \left(\frac{7 \pi}{3}\right)$

$= - 2 \cos \left(\frac{7 \pi}{3} - 2 \pi\right)$

$= - 2 \cos \left(\frac{7 \pi - 6 \pi}{3}\right)$

$= - 2 \cos \left(\frac{\pi}{3}\right)$

$= - 2 \left(\frac{1}{2}\right) = - 1$

$y = r \cos \theta$

$= - 2 \sin \left(\frac{7 \pi}{3}\right) = - 2 \sin \left(\frac{\pi}{3}\right) = - 2 \left(\frac{\sqrt{3}}{2}\right) = - \sqrt{3}$

The Cartesian form is $\left(- 1 , - \sqrt{3}\right)$